- Let’s plug in for a minimum player count of 2.
\begin{align*}
\hat{\text{rating}} &= 6.46 -0.17 \text{ min. players} + 0.32 \text{ time} - 0.02 \text{ min. players $\times$ time} \\
&= 6.46 -0.17(2) + 0.32 \text{ time} - 0.02 (2) \text{ time} \\
&= 6.46 -0.34 + 0.32 \text{ time} - 0.04 \text{ time} \\
&= (6.46 -0.34) + (0.32 - 0.04) \text{ time} \\
&= 6.12 + 0.28 \text{ time}
\end{align*}
- Let’s plug in for a minimum player count of 4.
\begin{align*}
\hat{\text{rating}} &= 6.46 -0.17 \text{ min. players} + 0.32 \text{ time} - 0.02 \text{ min. players $\times$ time} \\
&= 6.46 -0.17(4) + 0.32 \text{ time} - 0.02 (4) \text{ time} \\
&= 6.46 -0.68 + 0.32 \text{ time} - 0.08 \text{ time} \\
&= (6.46 -0.68) + (0.32 - 0.08) \text{ time} \\
&= 5.78 + 0.24 \text{ time}
\end{align*}
- Thus, we have the two models,
\begin{align*}
\hat{\text{rating}}_{\text{player = 2}} &= 6.12 + 0.28 \text{ time} \\
\hat{\text{rating}}_{\text{player = 4}} &= 5.78 + 0.24 \text{ time}
\end{align*}